(1 point) Rework problem 23 from section 2.4 of your text involving congressional committees. Assume that the committee consists of 11 Republicans and 6 Democrats. A subcommittee of 4 is randomly selected from all subcommittees of 4 which contain at least 1 Democrat.
What is the probability that the new subcommittee will contain at least 2 Democrats?

Step 1 ：Calculate the total number of ways to form a subcommittee of 4 from 11 Republicans and 6 Democrats. This is given by \(\binom{17}{4} = 2380\).

Step 2 ：Calculate the number of ways to form a subcommittee of 4 with at least 2 Democrats. This can be broken down into two cases:

Step 3 ：Case 1: The subcommittee has exactly 2 Democrats. There are \(\binom{6}{2}\) ways to choose the 2 Democrats and \(\binom{11}{2}\) ways to choose the 2 Republicans. So there are \(\binom{6}{2} \times \binom{11}{2} = 15 \times 55 = 825\) ways for this case.

Step 4 ：Case 2: The subcommittee has more than 2 Democrats. This can be either 3 or 4 Democrats. For 3 Democrats, there are \(\binom{6}{3} \times \binom{11}{1} = 20 \times 11 = 220\) ways. For 4 Democrats, there are \(\binom{6}{4} = 15\) ways (since all 4 members of the subcommittee are Democrats).

Step 5 ：Adding these up, there are \(825 + 220 + 15 = 1060\) ways to form a subcommittee of 4 with at least 2 Democrats.

Step 6 ：The probability that the new subcommittee will contain at least 2 Democrats is therefore \(\frac{1060}{2380} = \frac{53}{119}\).

Step 7 ：So, the final answer is \(\boxed{\frac{53}{119}}\).